Question

If the hypotenuse of a right triangle is 10 inches long and one of its legs is 5 inches long, how long is the other leg?

Answer 1

`5√(3)` inches long is the other leg

Explanation:

Given the statement: If the hypotenuse of a right triangle is 10 inches long and one of its legs is 5 inches long.

Hypotenuse side = 10 inches

Let length of other leg be x.

Pythagoras theorem states that in a right angle triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides.

Then; by definition of Pythagoras theorem;

`{\text}(Hypotenuse)^2 = (5)^2 + x^2`

`(10)^2 = 5^2 + x^2`

`100 = 25 + x^2`

Subtract 25 on both sides we get;

`100-25= 25 + x^2-25`

Simplify:

`75 = x^2`

Simplify:

`x = √(75) = 5√(3)` inches

Therefore, the sides of other leg is
`5√(3)` inches